Details

Time bar (total: 28.7s)

sample160.0ms

Algorithm
intervals
Results
60.0ms82×body1280valid
53.0ms29×body2560valid
16.0ms48×body640valid
5.0ms107×body80valid
5.0ms25×body320valid
3.0ms73×body80nan
1.0ms12×body160valid

simplify4.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01015
12515
26015
314315
435515
5107715
6442915
done500015

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.9b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.3b
(pow (+ 1.0 (/ i n)) n)
10.2b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
320×times-frac
305×add-sqr-sqrt
222×*-un-lft-identity
156×add-cube-cbrt
96×associate-*r*
84×difference-of-squares
48×unpow-prod-down
33×sqr-pow
28×distribute-lft-out--
24×prod-diff
19×add-exp-log
18×add-cbrt-cube
17×div-inv
13×associate-/r*
8×fma-neg
7×pow1 associate-/l*
6×cbrt-undiv div-exp add-log-exp
5×distribute-lft-out
4×expm1-log1p-u log1p-expm1-u
3×pow-unpow associate-*l* prod-exp cbrt-unprod unswap-sqr
2×flip3-- associate-/r/ flip-- associate-/l/
1×pow-to-exp sub-neg pow-pow frac-2neg diff-log div-sub associate-*r/ pow-prod-down pow-exp clear-num *-commutative
Counts
4 → 321
Calls
4 calls:
444.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
348.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
32.0ms
(pow (+ 1.0 (/ i n)) n)
464.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.7s

Counts
4 → 12
Calls
4 calls:
605.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
315.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
292.0ms
(pow (+ 1.0 (/ i n)) n)
503.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify2.4s

Counts
333 → 333
Iterations

Useful iterations: done (2.4s)

IterNodesCost
04797415
112756800
239406406
done50006350

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 17.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n)))
0.1b
(* 100.0 (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
11.9b
(* (pow i 2) (log 1.0))
18.2b
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
102×add-sqr-sqrt
87×add-cube-cbrt *-un-lft-identity
48×associate-*r*
23×add-exp-log
20×add-cbrt-cube
13×associate-/r*
11×associate-*l*
9×div-inv
7×pow1 unswap-sqr
6×cbrt-undiv log-prod div-exp prod-exp
4×expm1-log1p-u unpow-prod-down cbrt-unprod log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in associate-/l*
2×associate-/r/ *-commutative associate-/l/ unpow2 sqr-pow
1×pow-to-exp flip3-- frac-2neg div-sub associate-*r/ pow-prod-down pow-exp clear-num log-pow flip-- fma-udef
Counts
4 → 189
Calls
4 calls:
0.0ms
(fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n)))
38.0ms
(* 100.0 (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
20.0ms
(* (pow i 2) (log 1.0))
21.0ms
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

series843.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n)))
320.0ms
(* 100.0 (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
232.0ms
(* (pow i 2) (log 1.0))
246.0ms
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify1.5s

Counts
201 → 201
Iterations

Useful iterations: done (1.4s)

IterNodesCost
03296419
18256201
229905750
done50005741

prune1.0s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 7.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n)
0.1b
(* 100.0 (* (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
11.2b
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
11.9b
(* (pow i 2) (log 1.0))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×add-cube-cbrt *-un-lft-identity
25×add-exp-log
24×associate-*l*
22×add-cbrt-cube
19×times-frac
12×pow1
10×prod-exp
8×associate-*r* cbrt-unprod
6×log-prod unswap-sqr
4×expm1-log1p-u unpow-prod-down pow-prod-down log1p-expm1-u add-log-exp
3×cbrt-undiv distribute-rgt-in distribute-lft-in div-exp associate-/r* *-commutative associate-/l*
2×associate-*l/ div-inv associate-/l/ unpow2 sqr-pow
1×pow-to-exp flip3-- frac-2neg div-sub associate-*r/ pow-exp clear-num log-pow flip--
Counts
4 → 125
Calls
4 calls:
24.0ms
(* (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n)
60.0ms
(* 100.0 (* (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
31.0ms
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
18.0ms
(* (pow i 2) (log 1.0))

series1.3s

Counts
4 → 12
Calls
4 calls:
251.0ms
(* (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n)
290.0ms
(* 100.0 (* (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
187.0ms
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
578.0ms
(* (pow i 2) (log 1.0))

simplify1.4s

Counts
137 → 137
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02203686
15273611
217393100
done50013062

prune619.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 7.5b

localize35.0ms

Local error

Found 4 expressions with local error:

11.2b
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
11.9b
(* (pow i 2) (log 1.0))
11.9b
(* (pow i 2) (log 1.0))
11.9b
(* (pow i 2) (log 1.0))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
45×add-sqr-sqrt
27×add-cube-cbrt *-un-lft-identity
24×associate-*l*
21×add-exp-log
18×log-prod
12×unpow-prod-down associate-*r* add-cbrt-cube unswap-sqr
9×distribute-rgt-in distribute-lft-in times-frac prod-exp
7×pow1
6×unpow2 sqr-pow
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-to-exp pow-exp associate-/r* log-pow *-commutative cbrt-unprod associate-/l*
2×associate-/l/
1×cbrt-undiv flip3-- frac-2neg div-sub div-exp clear-num flip-- div-inv
Counts
4 → 140
Calls
4 calls:
17.0ms
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
15.0ms
(* (pow i 2) (log 1.0))
23.0ms
(* (pow i 2) (log 1.0))
22.0ms
(* (pow i 2) (log 1.0))

series759.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
201.0ms
(* (pow i 2) (log 1.0))
230.0ms
(* (pow i 2) (log 1.0))
182.0ms
(* (pow i 2) (log 1.0))

simplify2.6s

Counts
152 → 152
Iterations

Useful iterations: done (2.6s)

IterNodesCost
01382322
12952227
29141986
340981972
done50001969

prune677.0ms

Pruning

20 alts after pruning (18 fresh and 2 done)

Merged error: 7.5b

regimes237.0ms

Accuracy

57% (10.9b remaining)

Error of 19.2b against oracle of 8.3b and baseline of 33.7b

bsearch252.0ms

Steps
ItersRangePoint
11
0.0033763382367094055
5.206713059748268e+29
0.10387405912847383
5
-2.921513544512531
-0.7794201341187467
-0.9131486383075667

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03665
14665
done4665

end0.0ms

sample6.1s

Algorithm
intervals
Results
2.3s961×body2560valid
2.1s2473×body1280valid
658.0ms1602×body640valid
210.0ms3083×body80valid
208.0ms822×body320valid
132.0ms2281×body80nan
92.0ms429×body160valid
33.0ms8×body5120valid